Wednesday
January 28, 2015

# Homework Help: Math: Calculus

calculus 2
Find all points of intersection of the given curves. (Assume 0 ≤ θ ≤ 2π. Order your answers from smallest to largest θ. If an intersection occurs at the pole, enter POLE in the first answer blank.) r = 1 − cos θ, r = 1 + sin θ
Tuesday, December 2, 2014 at 8:32pm

Calculus
Differentiate. e^cos(x^2+1) Is the answer -2xe^cos(x^2+1) sin(x^2+1)?
Monday, December 1, 2014 at 10:10pm

calculus
Let f'(x)=4x^3-12x^2. (a) find three different functions with derivative equal to f'(x). how are the graphs of the three functions related? the only one that i can figure out is: f(x)=x^4+4x^3+y where y can equal any constant. any help on figuring out the other two ...
Monday, December 1, 2014 at 10:01pm

calculus
When a ball is thrown vertically upward into the air with a velocity of 79 ft/sec its height, y(t), in feet after t seconds is given by y(t) = 79t − 16t 2 . Find the average velocity of the ball over the interval from 3 to 3 + h seconds, h 6=/= 0. 1. average vel. = &#...
Monday, December 1, 2014 at 9:21pm

calculus
I needed help with these FRQ in my APCalc course. Any help or walkthrough would be extremely helpful - thanks in advance. Let f be the function given by f(x)=3ln((x^2)+2)-2x with the domain [-2,4]. (a) Find the coordinate of each relative maximum point and each relative ...
Monday, December 1, 2014 at 9:15pm

General Calculus Question
On a graph what ways can it not be differentiable? I know at cusps it's not differentiable but are there other instances where it is not differentiable?
Monday, December 1, 2014 at 9:14pm

Calculus
Water is being poured into a spherical bowl of radius 4cm at a rate of 2cm3/s. How fast is the water level rising when it is at 2cm?
Monday, December 1, 2014 at 7:24pm

calculus, help!
Evaluate the definite integral: int_{1}^{e^9} \frac{dx}{x \sqrt{\ln x}} = i gt my answer as 1^(e^9) but it's saying it's wrong
Monday, December 1, 2014 at 3:42pm

Calculus
consider the function f(x) = (x if x<1 (1/x if x>or equal to 1 Evaluate the definite integral: int_{-2}^{3} f(x)\,dx =
Monday, December 1, 2014 at 2:27pm

Calculus
Which of the following functions does not have a derivative of zero? A. y=-1/100 B. y=4(pi)^2-9 C. y=sin^2x+cos^2x D. y=cscxtanxcosx E. All do
Monday, December 1, 2014 at 11:12am

Calculus
Estimate the area under the graph of f(x)= x^2 + 2 x from x=1 to x=5 using 4 approximating rectangles and left endpoints.
Monday, December 1, 2014 at 10:50am

Calculus...help
The projected public spending by the British government for the years 2010-2011 (t = 0) through 2014-2015 (t = 4) is 692 billion pounds/year. The projected public revenue for the same period is f(t) = 292.6t + 134.4 / t + 6.9 + 500 billion pounds (0 ge t ge 4). Find the ...
Monday, December 1, 2014 at 12:02am

calculus
The number of U.S. citizens 65 and older from 1990 through 2050 is estimated to be growing at the rate of, R(t)=0.063t^2 -0.48t+3.87, (0 less than or = t less than or = 15) million people/decade, where t is measured in decades and t = 0 corresponds to 1900. Show that the ...
Sunday, November 30, 2014 at 11:50pm

Differential equations in Calculus...plsssss help?
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 at 11:42pm

Calculus
Find the limit as x approaches 1 5/(x-1)^2 I don't understand how to solve it because there would be a 0 on the denominator.
Sunday, November 30, 2014 at 11:09pm

Calculus
Find dy/dx if x^2+y^2=2xy A. x/(x-y) B. (y+x)/(y-x) C. 1 D. -x/y E. None of these
Sunday, November 30, 2014 at 10:43pm

Calculus with Diffrential Equations: Pleease help?
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 at 8:45pm

Calculus
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 at 8:30pm

Help with differential eqs problem???? (Calculus)
Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the grocery store, the height h of the bananas is ...
Sunday, November 30, 2014 at 7:49pm

Calculus
The slope of the line tangent to the curve xy+(y+1)^2=6 at the point (2, 1) is
Sunday, November 30, 2014 at 7:47pm

AP Calculus
For which of these functions f(x) does limit as x approaches negative infinity f(x)=2 A. (x-2)/(3x-5) B. 2x/sqrt(x-2) C. (2x^2-6x+1)/(1+x^2) D. (2x-1)/(x^2+1) E. None of these
Sunday, November 30, 2014 at 7:30pm

Calculus
Find limit as x approaches 5 (x^2-3x-10)/(x-5)
Sunday, November 30, 2014 at 6:03pm

AP Calculus
Find the derivative for f(x)=-x^2+x Do I put -x^2 on the denominator? How would I solve it if that's the case?
Sunday, November 30, 2014 at 5:58pm

Calculus
Find limit as x approaches -1 (x^2+2x+3)/(x^2+1) A. 0 B. 1 C. Infinity D. DNE E. None of these
Sunday, November 30, 2014 at 5:55pm

AP Calculus
Find f'(x): f(x)=(x^2-3x)/x^2 A. 2x-3/x^2 B. 2x-3/2x C. 1-(3/x) D. 3/x^2 E. None of these I get confused on the simplifying part.
Sunday, November 30, 2014 at 5:53pm

AB Calculus
I figured out that part "A" is -3/8, but i can't figure out part 2, a or b. please explain and help. thanks. Sand is falling from a rectangular box container whose base measures 40 inches by 20 inches at a constant rate of 300 cubic inches per minute. a) how is ...
Sunday, November 30, 2014 at 5:24pm

AP Calculus
Find limit as x approaches 1 5/(x-1)^2 A. 0 B. Negative infinity C. 5/4 D. Infinity E. None of these
Sunday, November 30, 2014 at 2:59pm

Calculus
Find the derivative: f(x)=1/cubed root(3-x^3) A. -1/3(3-x^3)^4/3 B. x^2/(3-x^3)^4/3 C. -x^2/(3-x^3)^2/3 D. -x^2/(3-x^3)^4/3 E. None of these
Sunday, November 30, 2014 at 1:50pm

Calculus
If f(x)=x^2+1 and g(x)=2x-1, find d/dx[f'(g(x))] at x=1 A. 2 B. 6 C. 4 D. 0 E. None of these
Sunday, November 30, 2014 at 12:30pm

AP Calculus
Find all points on the graph of f(x)=-x^3+3x^2-2 where there is a horizontal tangent line.
Sunday, November 30, 2014 at 12:23pm

Calculus
Find the limit as x approaches 0 [(sqrt(x+9))-3]/x A. 0 B. 1 C. Infinity D. 1/3 E. None of these
Sunday, November 30, 2014 at 12:15pm

Calculus,Reaction rates
A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at 10 ft/s. If the bridge is 10 ft above the boat, how fast are the man and the boat separating 1 second later?
Sunday, November 30, 2014 at 11:58am

AP Calculus
Let f(7)=0, f'(7)=14, g(7)=1, g'(7)=1/7. Find h'(7) if h(x)=f(x)/g(x)
Sunday, November 30, 2014 at 11:58am

Calculus
Find the derivative of x^2f(x) A. x[xf'(x)+2f(x)] B. 2xf'(x) C. x[xf'(x) +2f'(x)] D. x^2f'(x) E. None of these
Sunday, November 30, 2014 at 11:53am

Calculus,reaction rates
A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same point at 2:00 PM travels north at 45 kph. Find how fast the two are separating at 4:00 PM?
Sunday, November 30, 2014 at 11:52am

Calculus
Find an equation of the tangent line to the graph of x^2+3y^2=4 at the point (1,1) A. y+1=-1/3(x+1) B. y-1=-x/3y(x-1) C. x+3y=2 D. y-1=-1/3(x-1) E. None of these
Sunday, November 30, 2014 at 11:42am

Calculus
Find the equation of the line that passes through (1,3) and is perpendicular to the line 2x+3y+5=0 A. 3x-2y+3=0 B. 2x+3y-11=0 C. 2x+3y-9=0 D. 3x-2y-7=0 E. None of these I got E?
Sunday, November 30, 2014 at 11:30am

Calculus (Cross Section) again
A half of a pepperoni stick is 10 cm long. Assume that a cross section perpendicular to the axis of the pepperoni at a distance x from the end if a circle of radius rad(3x). What is the volume of the pepperoni
Sunday, November 30, 2014 at 10:51am

Calculus (cross section)
A solid has a base bounded by x^2_y^2=36. Find the volume of the solid if every plane section perpendicular to the diameter is an isosceles triangle whose base is on the circle and whose height is 4 units
Sunday, November 30, 2014 at 10:44am

Calculus
If f(1)=4 and f'(1)=2, find an equation of the tangent line at x=1 A. y=2x+2 B. y=2x-2 C. y=4x-7 D. y=4x-2 E. None of these
Sunday, November 30, 2014 at 4:49am

Calculus
Find f'(x) if f(x)=sin^3(4x) A. 4cos^3(4x) B. 3sin^2(4x)cos(4x) C. cos^3(4x) D. 12sin^2(4x)cos(4x) E. None of these I got D using the chain rule?
Sunday, November 30, 2014 at 4:46am

Calculus
Which of the following describes the graph of y=|2x+6|? A. Only continuous B. Only differentiable C. Both A and B D. Not continuous, not differentiable E. Constant
Sunday, November 30, 2014 at 2:45am

Calculus
Find d^2y/dx^2 for y=(x+3)/(x-1) A. 0 B. y=-8/(x-1)3 C. y=-4/(x-1)^3 D. y=8/(x-1)^3 E. None of these I got a positive number but am not sure about the denominator in the second derivative.
Sunday, November 30, 2014 at 2:32am

Calculus
Find dy/dx for y=sin(x+y) A. 0 B. (cos(x+y))/(1-cos(x+y) C. cos(x+y) D. 1 E. None of these I know I'm supposed to use implicit differentiation but I'm not sure how to go about it with sin
Sunday, November 30, 2014 at 2:08am

Calculus
Find an equation of the tangent line to the graph of f(x)=xsinx when x=0. A. y=0 B. f'(x)=0 C. y=xcosx+sinx D. y=x E. None of these
Sunday, November 30, 2014 at 1:50am

AP calculus
Find values for x and/or y on the graph of x^2-2y^2+9x+8y-276=0 for which there is a vertical tangent line
Sunday, November 30, 2014 at 1:47am

Calculus
For which of these functions f(x) does limit as x approaches negative infinity f(x)=2 A. (x-2)/(3x-5) B. 2x/sqrt(x-2) C. (2x^2-6x+1)/(1+x^2) D. (2x-1)/(x^2+1) E. None of these
Sunday, November 30, 2014 at 1:41am

Calculus
Find limit as x approaches 5 (x^2-3x-10)/(x-5) A. 2 B. DNE C. 0 D. 7 E. None of these
Sunday, November 30, 2014 at 1:33am

Calculus
If f(x) = {x^2+3x-1, x<=2 and -3bx+3, x<2 , find the value of b in order for f to be continuous
Sunday, November 30, 2014 at 1:24am

Calculus
If f(x) = {x^2+3x-1, x<=2 and -3bx+3, x<2 , find the value of b in order for f to be continuous
Sunday, November 30, 2014 at 1:24am

Calculus
If f(x)=sin(2x), find f"(x) A. 2cos(2x) B. -4sin(2x) C. -2sin(2x) D. -4sinx E. None of these Is it B from using chain rules?
Sunday, November 30, 2014 at 1:21am

Calculus
Find the derivative for f(x)=-x^2+x Do I put the -x^2 as a denominator? How would I solve it if that's what I'm supposed to do?
Sunday, November 30, 2014 at 1:16am

Calculus
Find limit as x approaches -1 (x^2+2x+3)/(x^2+1) A. 0 B. 1 C. Infinity D. DNE E. None of these
Sunday, November 30, 2014 at 1:11am

Calculus
Find limit as x approaches 1 5/(x-1)^2 A. 0 B. Negative infinity C. 5/4 D. Infinity If I use limit as h approaches 0 f(x+h)-f(x)/h , will I get an x in the answer?
Sunday, November 30, 2014 at 12:55am

Calculus
Find dy/dx if x^2+y^2=2xy A. x/(x-y) B. (y+x)/(y-x) C. 1 D. -x/y E. None of these Do I equal it to 0 and use implicit rule?
Sunday, November 30, 2014 at 12:49am

Calculus
Find f'(x) for f(x)=(2x^2+5)^7 A. 7(4x)^6 B. 7(4x)^7 C. 28x(2x^2+5)^7 D. 7(2x^2+5)^6 E. None of these Would it be none of these because of the 4x in the chain rule?
Sunday, November 30, 2014 at 12:43am

Calculus
Determine the limit as x approaches 1 f(x) if f(x)={3-x, x does not equal 1 and 1, x=1 A. 2 B. 1 C. 3/2 D. DNE E. None of these
Sunday, November 30, 2014 at 12:38am

math calculus
convert these symmetric equations to parametric form: line 1:(x-1)/k = (y-2)/2 = (z+1)/k-1 and line 2: (x+3)/-2 = (z)/1, y=-1
Saturday, November 29, 2014 at 7:49pm

math calculus
For the function: f(x)= 2+x-x^2/ (x-1)^2 ; f'(x)= x-5/(x-1)^3 ; f''(x)=2x-14/(x-1)^4 a)find vertical and horizontal asymptotes. Examine vertical asymptote on either side of discontinuity. b)find any local extrema c)find points of inflection
Saturday, November 29, 2014 at 7:45pm

Pre-Calculus
You have been hired by the Humane Society to construct six animal cages using 1400 feet of chain fence. Express the length and width using function notation. Include a graph with the area function with explanation of significance. Find the dimensions that maximize the total ...
Friday, November 28, 2014 at 11:33pm

Calculus I
An open box with square base is to be constructed. The material for the base costs $10 per square foot. The material for the sides costs$1 per square foot. the box must have an area of 100 square feet. Find the dimensions of the box that minimize cost. What I have so far: A...
Friday, November 28, 2014 at 9:41pm

Calculus
What is the smallest possible slope for a tangent to y=x^3 - 3x^2 + 5x? (I'm unsure how to approach this problem, if you know how to solve it, please explain step by step. THANK YOU!!!)
Friday, November 28, 2014 at 7:22pm

Calculus
An aquarium is to be constructed to hold 2160 in3. The base is to made of slate and the sides of glass. If slate costs 5 times as much as the glass per sq in, find the dimensions that will minimize the cost of constructing the aquarium. I started going about this problem by ...
Friday, November 28, 2014 at 11:34am

calculus
Baseball Star Bryan is standing at the top of the Sears Tower in Chicago and decides to throw a baseball up with a velocity of 5 m/s. The Sears Tower is 442 meters tall and gravity exerts a constant acceleration of -9.8 m/s/s. Ignore ball mass and wind resistance. a.) Find ...
Friday, November 28, 2014 at 9:37am

Calculus
solve the differential equation dy / dx = 11x^2y^2 with the condition that y(0) = 4 The solution to the equation is y =
Wednesday, November 26, 2014 at 10:16am

Brief Calculus
Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. (Round your answer to four significant digits.) Enclosed by y = e^x, y = 2x + 1, x = −2...
Tuesday, November 25, 2014 at 8:43pm

Calculus
5) Evaluate the definite integral. On the integral from 1 to e^7 ∫dx/x(1+lnx)
Tuesday, November 25, 2014 at 11:16am

Calculus
2) If f(x)=∫t^2dt not he integral from 4 to x^3 then f′(x)=?
Tuesday, November 25, 2014 at 11:14am

Calculus
20) Evaluate the definite integral. On the integral from e to e^3 ∫dx/xl(nx)^(1/2)
Tuesday, November 25, 2014 at 11:13am

Calculus
The sales of Universal Instruments in the first t years of its operation are approximated by the function S(t) = t 0.96t2 + 25 where S(t) is measured in millions of dollars. What were Universal's average yearly sales over its first 5 years of operation?
Tuesday, November 25, 2014 at 1:05am

calculus
A) Determine the vector equation of the plane that contains the following two lines: l1: vector r= [4,-3,5] + t[2,0,3], tER l2: vector r= [4,-3,5] + s[5,1,-1], sER b)Determine the corresponding Cartesian equation.
Monday, November 24, 2014 at 10:57pm

math calculus
if i,j,k are the standard unit basic vectors, in 3 space, determine the value of k dot(j-3k)+(i-4k) dot (i-4k)-8 |i cross -k| (Simplify without using components)
Monday, November 24, 2014 at 6:48pm

calculus
(i know i've asked so many questions. i just want to make sure my answers are right for this homework! hopefully it isn't too annoying for you :) ) Find the derivative of the given function. y=(tan^-1)√(3x) A. (1)/(√(1-3x)) B. (1)/(6√(3x(1+3x))) C. (3...
Monday, November 24, 2014 at 6:26pm

calculus
Me again. One last question! Again, just needed my answer verified with any explanation or walk-through. The position of a particle moving along a coordinate line is s=√(3+6t) with s in meters and t in seconds. find the particle's acceleration at t=1 second. a. 1 m/...
Monday, November 24, 2014 at 6:14pm

Calculus
What does y'' mean in calculus? Is there a word for it? Also is there a word for f'(x)? Thanks.
Monday, November 24, 2014 at 5:46pm

calculus
hello! i just needed help to verify or falsify my answer and any explanation as to why would be extremely helpful! thanks ahead of time. y=(x^2)-6x+10 a. at x=3 b. at x=0 c. at x=1 d. at x=-3 my answer was D. thanks again!
Monday, November 24, 2014 at 4:59pm

calculus
hello! i just needed help to verify or falsify my answer and any explanation as to why would be extremely helpful! thanks ahead of time. y=(x^2)-6x+10 a. at x=3 b. at x=0 c. at x=1 d. at x=-3 my answer was D. thanks again!
Monday, November 24, 2014 at 4:58pm

Brief Calculus
Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = −x and y = −x^3 for x in [−1, 1]
Monday, November 24, 2014 at 2:31pm

Calculus
11) Find the following indefinite integrals. ∫x/(x+9)^(1/2)dx
Monday, November 24, 2014 at 10:14am

Calculus
10) Evaluate the integral by making the given substitution. ∫sec(5x)tan(5x)dx u=5x
Monday, November 24, 2014 at 10:13am

Calculus
9)Evaluate the indefinite integral. ∫x^8e^(x^9)dx
Monday, November 24, 2014 at 10:12am

Calculus
6) Evaluate the indefinite integral. ∫cosx/(7sinx+35)dx
Monday, November 24, 2014 at 10:11am

Calculus
5) Evaluate the definite integral. On the integral from 1 to e^7 ∫dx/x(1+lnx)=?
Monday, November 24, 2014 at 8:47am

Calculus
4) On the integral from 1 to 2 ∫(4x^2+4)/x^2dx =?
Monday, November 24, 2014 at 8:46am

Calculus
2) If f(x)=∫t^2dt on the interval from 4 to x^3 then f′(x)=?
Monday, November 24, 2014 at 8:44am

Calculus
h(t)= -16t^2 + v0t. How fast is the object moving after 5 seconds?
Sunday, November 23, 2014 at 9:20pm

Calculus
Use Riemann sums and limits to compute the area bounded by f(x) = 10x+9 and the x axis between x=10 to x =5 The area is = to
Sunday, November 23, 2014 at 1:41pm

Calculus
Find the x-values of all points where the function below has any relative extrema. Find the values(s)of any relative extrema. G(x)=(x-3)^2/x-4. How do I solve this?
Sunday, November 23, 2014 at 12:27pm

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves: 2x = -y^2 y^2 = -x + 2 y = 0 for y >= 0 about the x-axis. Not sure how to do this one, could anybody help me identify what this looks like and how to identify the outer/inner radius? Thanks
Sunday, November 23, 2014 at 3:17am

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves: y = x^2 and x = y^2 about the line y = 1. I received the answer pi/30, using the outer radius of (1 - x^2) and the inner radius of (1 - x^(1/2)). Is this correct?
Sunday, November 23, 2014 at 12:45am

Calculus
For f(x)= (x+3)^2/(4x-5) find all x such that f(x) increases.
Saturday, November 22, 2014 at 7:28pm

Calculus
Of the infinitely many lines that are tangent to the curve y = −7 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
Thursday, November 20, 2014 at 9:05pm

Pre Calculus
The logistic growth function P(t)= 160/ 1 + 9e^-0.165t describes the population of the endangered species of elk "t" years after they were introduced into the habitat. a. How many elk were initially introduced into the habitat? b. How many elk are expected after 6 ...
Thursday, November 20, 2014 at 3:43pm

Pre Calculus
If a 25 mg sample of radioactive material decays to 18.4 mg in 5 years, how long will it take the sample to decay to 20.5 mg?
Thursday, November 20, 2014 at 3:42pm

Pre Calculus
You invest \$4500 into an account that earns 6.5% interest compounded monthly. How long will it take for the account to double in its value?
Thursday, November 20, 2014 at 3:41pm

Pre Calculus
The population of a city is 127,000 and is decreasing by 2.4% each year. a. What will the population be in 10 years? b. Find when the population will be 95,000
Thursday, November 20, 2014 at 3:40pm

Pre-Calculus
Suppose person A collaborated with person B, who has collaborated with person C, who has collaborated with Paul Erdös. Suppose also that person B never collaborated with Paul Erdös and person A never collaborated with anyone with an Erdös number of 1 or less. ...
Thursday, November 20, 2014 at 2:12pm

Please check my answers and let me know if I did something wrong. Thank you! Find the partial derivative of x, and the partial derivative of y, then the partial derivative of x (1,-1), and the partal derivative of y (1,-1). f(x,y) = x^4 y^2 -x here is what I got @f/@x = 3x^3 y...
Thursday, November 20, 2014 at 9:30am

calculus
Consider a 10in by 14in rectangle to which you make square cuts of side length "x" in each corner, then fold the sides and form a box of height "x". What should "x" be to maximize the volume of the box?
Wednesday, November 19, 2014 at 9:34pm